Gravity

What is gravity?

Gravity is the force of attraction between masses. It’s a field force: it acts across empty space, without the objects touching. Earth pulls on you right now, even though no rope connects you to it.^[4]

Isaac Newton realised that the force that makes objects fall on Earth is the same force that holds the Moon and planets in their orbits. He described it in his law of universal gravitation.^[1]

Newton’s law of universal gravitation

Newton’s law says that the gravitational force between two bodies is:^[1]

F = G × M₁ × M₂ ÷ R²

• M₁ and M₂ are the two masses.
• R is the distance between them.
• G is a universal constant: the same number everywhere in the universe.

Two things follow:

• More mass, more pull. The attraction is proportional to the masses of both bodies.^[1]
• Distance weakens it fast. Because R is squared, a planet twice as far from the Sun would feel (1/2)², or 1/4 of the force. Three times farther, and it feels (1/3)², or 1/9.^[1] This is the inverse-square law.

Mass versus weight

Mass is how much matter something contains, and it’s the same wherever you go. Weight is the force of gravity on you, so it depends on the local strength of gravity.^[1] Stand on the Moon and your mass is unchanged, but your weight is much lower.

Why the Moon doesn’t fall down (it does)

The Moon is falling toward Earth, all the time. But it is also moving sideways so fast that, as it falls, the surface of Earth curves away beneath it. It falls around Earth instead of onto it.^[1]

Newton tested this idea with numbers. The Moon is about 60 Earth-radii away, so by the inverse-square law its acceleration toward Earth should be about 1/3,600 of the acceleration of a falling object on Earth’s surface. The measured value, about 0.00272 m/s², matches.^[1]

Newton imagined a cannon on a very high mountain. Fire a cannonball faster and faster, and it lands farther and farther away, until it’s fast enough to fall completely around Earth.^[2] That is exactly what satellites do.

Gravity and orbits

Newton showed that an inverse-square force of gravity produces exactly the kinds of orbits described by Kepler’s laws of planetary motion.^[1] He also found that the size and period of an orbit depend on the masses of both bodies.^[1] Explore Orbits and Kepler’s Laws for the details.

Tides: gravity stretching Earth

The Moon doesn’t pull equally on every part of Earth: the near side is pulled more than the far side. These differences distort Earth slightly and make the oceans bulge.^[3] Water piles up below the Moon and also on the opposite side, so a typical coast sees two high tides and two low tides a day.^[3]

• The Sun also raises tides, but it is less than half as effective as the Moon.^[3]
• When the Sun and Moon line up, their tides reinforce each other, giving extra-large spring tides. When they are at right angles (first and last quarter Moon), they partly cancel, giving smaller neap tides.^[3]
• Tides even affect Earth and the Moon over time. Tidal friction makes our day about 0.002 seconds longer each century, and the Moon is moving away from us by about 3.8 cm a year.^[3]

Common misconceptions

• “There’s no gravity in space.” Earth’s gravity reaches far into space: it extends all the way to the Moon, bending the Moon’s path into an orbit.^[1]
• “Heavier things fall faster.” A bigger mass does feel a bigger gravitational force, but it also needs more force to accelerate by the same amount (Newton’s second law). The two effects balance out.^{[5, 1]}